for a collection of finitely many
basis
functions
\(\psi _i^a, \psi _j^b\) —e.g.,
multivariate
Hermite polynomials, Hermite functions,
splines, or
radial basis functions—and
unknown
real valued coefficients \((a_{i},b_{j})\) .We may substitute the exponential
in
(REF ) with a
square function or even a sum of squares [1]}.
This offers the computational advantage of
precomputing any
integral in (REF ) once and
for all, thanks to
parameterizations of
\(b_k\)  that
is linear in the
unknown coefficients (see [2]}).
The minimization in
(REF )
can then be cast
in terms of
the unknown
coefficients, which fully
parameterize the maps in
\(\mathcal {H}_k\) .
